The network infrastructure of a known radio communications system, e.g. a system for cellular or telephony, includes a plurality of fixed, spaced-apart radio base stations (referred to as “stations”), each of which transmits signals to and receives signals from a plurality of mobile users, within its geographic coverage area.
FIG. 1 illustrates a network infrastructure of a typical radio communications system, comprising radio base stations R0, R1, R2, R3, R4. The system in FIG. 1 schematically illustrates a mobile unit U, such as a cellular telephone handset, which is served by a serving station R0. Each of the radio base stations R0, R1, R2, R3, R4 is associated with a respective operating range L0, L1, L2, L3, L4, which indicates an area in which the radio base station is capable of communicating with mobile units. As is clear from FIG. 1, the operating ranges may overlap within certain geographical areas. For example, in FIG. 1, the operating range of station R1 partially overlaps with the operating ranges of stations R0, R2 and R3, but not with station R4.
Each station may have a plurality of radio transmitters that communicate with mobile users over either a single frequency or, in the case of a synthesized frequency hopping radio transmitter, a plurality of frequencies. Because the plurality of stations are positioned at given intervals throughout the geographic area, communication signals, both downlink signals generated by a station and uplink signals generated by a mobile user, need only be of relatively low power levels for the base station and mobile user to effectively communicate with each other.
A significant advantage inherent in radio communications systems is the ability to reuse the available frequencies. A spectrum of available frequencies is typically assigned to a radio network operator of a radio communications system by a controlling authority. In a case where a number of radio network operators are to operate similar systems using similar equipment, there may be only a relatively narrow range of frequencies, which is to be distributed between the operators. Thus, each radio network operator need to utilize its available frequencies as efficiently as possible.
The relatively low power levels of the communication signals, allow the same frequencies to be allocated for communications in different stations within the radio communications system. Thus, the same frequency can be used concurrently at a plurality of locations throughout the geographical area of the radio communications system, which permits a plurality of different communications between a plurality of different mobile users to be carried out at the same frequency at any given time. For example, in FIG. 1 the stations R1 and R4 could be assigned the same frequencies, since their respective operating ranges L1, L4 do not overlap.
The stations whose communications are activated at the same frequencies must be carefully selected so that concurrent reuse of communication signals in the various stations do not interfere significantly with one another. If frequencies are reused at locations that are too close to one another, interference between the signals transmitted on the same frequencies might result.
In order to optimize the performance of radio communications systems it is important to predict accurately how the reuse of frequencies impacts the quality-of-service in the network.
Quality-of-service may be expressed in terms of a carrier-to-interference ratio between the signal strength from a serving station and the compound of signal strengths from one or many interfering stations, or by mapping this carrier-to-interference ratio to a probability of interference. Typically, the quality-of-service is specific to each physical location within the geographic area served by the radio communications network.
It is known, from e.g. Halonen, T. et al.: GSM, GPRS and EDGE Performance-Evolution Towards 3G/UMTS, John Wiley & Sons, Ltd., 2002, page 575, to predict quality-of-service by deriving carrier-to-interference ratios for a carrier frequency k where a plurality of interfering signals Ijk are received from a plurality of interfering stations j, by a signal strength comparison between a carrier signal at the carrier frequency k and the compound of all interfering signals Ijk at this same k frequency and adjacent frequencies k±1. The interfering signals at adjacent frequencies are considered after attenuation by a factor that reflects the level of interference at a frequency from an adjacent frequency in the technology of the present radio communications system. By an “adjacent frequency” is meant any frequency, other than the predetermined frequency, which is capable of interfering with e.g. the carrier frequency. This could be expressed by the following formula:CIRk=Ck/(Σj(Ijk+adj*(Ij,k−1+Ij,k+1))+N0)  (1),wherein:    CIRk is the carrier-to-interference ratio at carrier frequency k;    Ck is the serving signal strength at carrier frequency k;    ΣjIjk is the sum of all signal strengths from interfering stations j at frequency k;    adj is the adjacent frequency protection on the first adjacent carrier frequency; and    N0 is the receiver noise floor.
U.S. Pat. No. 6,405,043 B1 discloses a method of deriving the interference at a carrier frequency with consideration of transmission probabilities of the stations, where the frequency assignments have been allocated. However, the method described in U.S. Pat. No. 6,405,043 B1 is not applicable in a situation when frequency assignments have not been allocated.
It is also known from e.g. Snyman, M.: The Challenges of Obtaining an Accurate Model of your Network for Input to AFP Tools, Optimizing GSM Networks, Conference Proceedings, IIR ltd., 1999, page 2 ff, to predict quality-of-service at carrier frequency by mapping the carrier-to-interference ratio to a probability of interference using a CIR-weights function, ciw (CIRk).
FIG. 2 provides an example of a known CIR-weights function for mapping from carrier-to-interference ratio to probability of interference. The ciw-function of FIG. 2 provides a mapping of a carrier-to-interference ratio in dB (x-axis) to a probability of interference (y-axis). The figure indicates the probability of interference in case of reuse on the same frequency (co-curve—right curve) and adjacent frequency (adj-curve—left curve).
There are several procedures that use quality-of-service predictions in the design and optimization of a radio communications system, such as a mobile network.                Cell planning procedures are used to optimize the quality-of-service by configuring the stations in the radio communications system.        Capacity planning procedures aim at predicting the quality-of-service for a given level of capacity growth, or at determining a possible capacity growth before the quality-of-service is degraded to a predetermined minimum value.        Frequency planning procedures are used to optimize quality-of-service by efficiently assigning the frequencies that are available to the radio network operator.        
In cell planning procedures, the frequency assignments of the stations have typically not yet been allocated. Instead stations, each serving a particular geographic area, referred to as a cell, are typically placed and configured without any consideration of the frequency assignments. The rationale behind this is that the frequency parameters are relatively easy to change in radio communications systems and are therefore assigned after the stations have been placed and configured. Thus, a frequency planning procedure will have to take place subsequent to the cell planning procedure. The configurations of the stations within the radio communications system will therefore be unbiased in terms of their frequency assignments.
With additional mobile users added to the radio communications system, it is required that additional radio transmitters and thereby frequencies are allocated to the stations. In capacity planning procedures, when e.g. additional capacity in terms of new stations and/or radio transmitter are added to an existing system, such stations and/or radio transmitters need to be assigned frequencies. However, to accommodate these new frequency requirements it is typically necessary to reallocate the frequency assignments of all radio transmitters in the area, subject to this capacity growth in order to ensure a good overall frequency plan in this area.
Frequency planning procedures aim at allocating frequencies optimally in radio communications systems. This is typically an iterative process, wherein frequencies are manually assigned, evaluated and then reassigned, depending on the outcome. In this process, station relationships are used as indications of how communications are impacted in case any pair of two stations reuses either the same or adjacent frequencies. This impact is expressed either as the amount of traffic (Erlangs) or as the amount of area (square kilometers or square miles) that would be interfered if the two stations reused. Note that the frequency assignments of the stations have not yet been allocated when the station relationships are derived. The calculation is solely based on the assumption that the serving and interfering station are reusing frequencies, without specifying which specific frequencies they are reusing. An algorithm is known for deriving these station relationships by aggregating over all locations the mapping of signal strength comparisons between pairs of a serving station and a single interfering station to interference probabilities.
This known algorithm is outlined below with reference being made to FIG. 3.
In step S0, traffic (ticij, tiaij) and area (aicij, aiaij) accumulators are initially set to zero. These accumulators identify the amount of traffic/area that would be interfered if a serving station i and an interfering station j reuse either the same frequency or adjacent frequencies.
In step S1, a location is selected for evaluation.
Step S2 constitutes a sub-step of step S1, which comprises identifying and evaluating a serving station i at this location, with the probability of serving at this location equal to spi.
Step S3 is a sub-step of step S2, and comprises evaluating each station j which interferes with the serving station i at this location.
In step S4, lpc, the probability of interference at the location assuming reuse with station j on the same frequency is calculated: lpc=spi*(ciw(Ci/Ij)).
In step S5, lpa, the probability of interference at the location assuming reuse with station j on adjacent frequencies is calculated: lpa=spi*(ciw(Ci/Ij−adj)).
In step S6, the amount of traffic that would be interfered at this location on the same frequency, ticij, and on adjacent frequencies, tiaij, is added to the traffic accumulators:ticij=ticij+lpc*lt; tiaij=tiaij+lpa*lt. 
In step S7, the amount of area that would be interfered at this location on the same frequency, ticij, and on adjacent frequencies, tiaij, is added to the area accumulators:aicij=aicij+lpc*la; aiaij=aiaij+lpa*la. 
In step S8, the flow returns to step S3 in case there are more interfering stations at the present location.
In step S9, the flow returns to step S2 in case there are more serving stations at the present location.
In step S10, the flow returns to step S1 in case there are more locations to evaluate.
In step S11, the flow terminates, with the traffic (ticij, tiaij) and area (aicij, aiaij) accumulators as the derived result between all combinations of a serving station i and an interfering station j.
In the above described algorithm, the following abbreviations are used:    ticij designates traffic interfered if station i reuse with station j on the same frequency,    tiaij designates traffic interfered if station i reuse with station j on adjacent frequencies,    aicij designates area interfered if station i reuse with station j on the same frequency,    aiaij designates area interfered if station i reuse with station j on adjacent frequencies,    Ci expresses the signal strength of serving station i at the location in dBm,    Ij expresses signal strength of interfering station j at the location in dBm,    adj represents in dB how much a frequency interferers with an adjacent frequency in the technology used by the radio communications system,    lt expresses the amount of traffic at the location in Erlangs, and    la expresses area of the location in e.g. square kilometers or square miles.
A limitation in this known way of deriving station relationships is that it calculates the carrier-to-interference ratio between a serving station and a single interfering station without consideration of how other interfering stations affect this carrier-to-interference ratio. The problem with this method is that the station relationships do not accurately estimate the negative impact when a serving station and an interfering station are reusing frequencies.
A common problem to all the above-described cell, capacity and frequency planning procedures is that any quality-of-service prediction needed in these procedures require that a frequency plan is known. This is a significant disadvantage, as it is a very time consuming and labor intensive exercise to produce a frequency plan. The problem of evaluation of the expected quality-of-service due to stations configurations in cell planning processes and capacity expansions in capacity planning processes is aggravated by the fact that it is very difficult to find the theoretically optimal frequency plan, which means that this estimation will be dependent on the quality of a frequency plan, which is not only very difficult to find but which also does not guarantee that the quality-of-service of such a plan will represent the best quality-of-service of the network.